A note about words which coincide except in one position

TL;DR

This paper corrects a false statement in algebraic combinatorics on words, providing a modified result that enables fixing a related theorem's proof.

Contribution

It identifies a false claim in existing literature and offers a corrected version to ensure the validity of related proofs.

Findings

Original result was false

Modified statement corrects the previous error

Enables fixing of a related theorem's proof

Abstract

In this short note, we show that a result about words which coincide except in one position given as an exercise in Lothaire's Algebraic Combinatorics on Words is false. Moreover, we derive a modified statement which allows us to fix the proof of a theorem which originally used the result of this exercise.